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 which, I maintain, is the only expedient that can be practised with a mathematical certainty of being safe: these, and many other important secrets, I am ready, at any time when called upon, to communicate. One I cannot even now withhold, which is this: that there is no good or truly geometrical riding, unless the legs be extended perfectly in straight lines, so as to form tangents to the cylindrical surface of the horse's body: in a word, to resemble, as much as possible, a pair of compasses set astride upon a telescope; which I conceive to be the perfect model of mathematical riding.

But besides this application of pure geometry, it has often struck me, that too little use is made, in riding, of the principles of mixed mathematics. Consider, Mr. Gambado, the six mechanical powers! the lever, the wheel and axle, the pulley, the inclined plane, the wedge, and the screw; and reflect with what advantage all these may be applied to the uses of Horsemanship. By means of a lever, having an elevated fulcrum raised